Sure, but that's still "a scanner attached to a modem." Nothing about a scanner implies that it must buffer the input, just like nothing about a printer implies that it buffers the output.
There are/were "line printers" doing "latch a character from the input line, print the character, unlatch" serial output (which were so common that Unix pipes are designed around the foibles of outputting to such devices.) Most POS thermal receipt printers are still line printers!
I don't know as much about scanners, but I can't imagine that the original (digital, attached to a computer) scanners weren't also "serial scanners"—i.e., rather than a 1D scan head with a long CCD strip that could latch an entire line at a time into a shift register, they would have had 2D scan-heads that would scan one pixel at a time, in a "read brightness, signal ready, wait for return line to unlatch" serial loop. No memory required, just terribly slow.
When the relevant laws were made, fax machines were purely analog devices, not a scanner attached to a modem. And once fax was legally privileged, it stuck around exactly because it was legally privileged - despite the change in technology.
> fax machines were purely analog devices, not a scanner attached to a modem
Why would an analog scanner not still be a scanner? I'd call whatever component that's in even the oldest fax machines "a scanner." Even if it is "enitrely analog" (continuous brightness intensity read, like a tape head or record-player stylus) you'd still call the process of converting light from a sensor passing over a document, into electricity, scanning, and you'd still call the component that does that "a scanner." Just like speakers and microphones are still "speakers" and "microphones" whether they're just transducers attached to wires, or have a whole ADC+USB/Bluetooth signal path leading out of them. Am I wrong?
Yes, in the same sense that an analog telephone is recording you by translating your voice into electricity. But, at least to me, if it is voice -> electricity on wire -> speaker, it feels much less like recording than saving a buffer of voice in memory, packetizing, and then sending, even if they are both just electricity on a wire.
